Improved bounds for the sunflower lemma
成果类型：
Article
署名作者：
Alweiss, Ryan; Lovett, Shachar; Wu, Kewen; Zhang, Jiapeng
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2021.194.3.5
发表日期：
2021
页码：
795-815
关键词：
摘要：
A sunflower with r petals is a collection of r sets so that the intersection of each pair is equal to the intersection of all of them. Erdos and Rado proved the sunflower lemma: for any fixed r, any family of sets of size w, with at least about w(w) sets, must contain a sunflower with r petals. The famous sunflower conjecture states that the bound on the number of sets can be improved to c(w) for some constant c. In this paper, we improve the bound to about (log w)(w). In fact, we prove the result for a robust notion of sunflowers, for which the bound we obtain is sharp up to lower order terms.